Flow, Heat And Mass Transfer Of Oldroyd-B Fluid And Pseudo-plastic Fluid Over A Stretching Surface

Viscoelastic fluid and power-law fluid have been widely employed in production and life,such as chemical process,food processing,plastic stretching and oil exploitation,etc.The constitutive relation of Oldroyd-B fluid takes the characteristics of time relaxation and delay into account,which can reflect the rheological properties of viscoelastic fluid.Pseudo-plastic fluid is a kind of power-law fluid,which can show the characteristics of shear thinning.In this paper,the stagnation point flow,heat and mass transfer of Oldroyd-B fluid and the boundary layer flow,heat and mass transfer of pseudo-plastic fluid over stretching surface are discussed.The xanthan gum aqueous solution with pseudo-plastic fluid and viscoelastic fluid characteristics is also analyzed experimentally.The first part is devoted to the exploration of stagnation-point flow of Oldroyd-B MHD nanofluids over stretching surface.On the one hand,the constitutive relation of Oldroyd-B fluid is deduced by upper convective derivative.On the other hand,Cattaneo-Christov double diffusion model is introduced in the process of heat transfer and mass diffusion.The approximate analytical solution is obtained by a newly analytical method combining the double-parameter transformation expansion method with the base function method(DPTEM-BF)after clever similarity transformation.And the effects of the physical parameters on the stagnation point flow,heat and mass transfer are analyzed.In the second part,the flow,heat and mass transfer of pseudo-plastic fluid over stretching surface are investigated.Double-power-law Fourier's law and Fick's law are established to simulate the process of heat transfer and mass diffusion by assuming that the heat flux is power-law-dependent on both velocity gradient and temperature gradient,and the mass flux is power-law-dependent on both velocity gradient and concentration gradient.Meanwhile,the double-power-law diffusion model is also introduced into the convective heat and mass transfer boundary conditions.For the governing equation of the double-power-law flow,heat and mass transfer of pseudo-plastic fluid,it is transformed into ordinary differential equations by similarity transformation,and then the approximate analytical solution is obtained by the differential transform method and the base function method(DTM-BF).The influences of physical parameters on flow,heat transfer and mass diffusion are revealed by the solutions.In the third part,the experimental analysis is carried out.A new constitutive relationship is established by combining the pseudoplasticity and viscoelasticity of xanthan gum aqueous solution.The shear stress and shear rate of xanthan gum solution at different time points during shear movement were measured by MCR rheometer.Measured data were fitted with new constitutive relationship to determine the physical parameters,and the Maxwell-power-law constitutive model and Oldroyd-B-power-law constitutive model were obtained.